Gain Spectra of Quantum Wires with Inhomogeneous Broadening

The effects of fabricational variations on the gain spectra of quantum wires are calculated within the limits of first order perturbation theory. Gain spectra and density of states for 50 A radius and 150 A radius cylindrical quantum wires are calculated and plotted for several different fabrication tolerances. The wave functions for a finite, cylindrical potential are calculated and a quasi-critical radius, below which the carriers are weakly confined by the potential, is established. This sets a lower limit on quantum wire size. Upper limits on the size of quantum wells, quantum wires, and quantum boxes are also discussed. The threshold current and differential gain of quantum wire lasers and quantum wire array lasers are calculated. These calculations indicate a possible reduction in threshold current of one to two orders of magnitude as compared to the best quantum well lasers.